Kabul - Thousands of protesters took to the streets of the Afghan capital on Monday, setting fire to cars and shouting "death to America", the latest in demonstrations that have swept the Muslim world against a film mocking the Prophet Mohammad.

Western embassies across the Muslim world are on high alert and the United States has urged vigilance after days of anti-American violence provoked by the film.

"There were between 3,000 and 4,000 demonstrators. They burned some police cars, but we could split them up and prevent the insecurity widening," Lieutenant-General Fahem Qayem, police quick reaction force commander, told Reuters in Kabul.

Embassies in Kabul's heavily guarded central zone were placed on lockdown, including the U.S. and British missions, after violence flared near fortified housing compounds for foreign workers in the city's volatile eastern suburbs.

"We will defend our prophet until we have blood across our bodies. We will not let anyone insult him," said protester Jan Agha Pashtun, giving what was apparently a false name to avoid police retaliation. "Americans will pay for their dishonor."

It was the latest in a week of violent protests fanned by anger over a video, posted on the Internet under several titles including "Innocence of Muslims", that mocked the Prophet Mohammad and portrayed him as a womanizer and a fool.

The head of Libya's national assembly said an attack on the U.S. consulate in Benghazi that killed Ambassador Christopher Stevens and three other Americans last Tuesday looked like a planned assault by a "group with an agenda" rather than a spontaneous reaction to the video posted online.